What is the integral from 0 to 5 of xcos(x) ?

The integral from 0 to 5 of xcos(x) is 5sin(5)+cos(5)-1

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integral from 0 to 5 of xcos(x)

\int_{0}^{5} x cos (x) d x

5 sin (5) + cos (5) - 1

Decimal

- 5.51095 \dots

Solution steps

\int_{0}^{5} x cos (x) d x

Apply Integration By Parts

= [x sin (x) - \int sin (x) d x]_{0}^{5}

\int sin (x) d x = - cos (x)

= [x sin (x) - (- cos (x))]_{0}^{5}

Simplify

= [x sin (x) + cos (x)]_{0}^{5}

Compute the boundaries:

5 sin (5) + cos (5) - 1

= 5 sin (5) + cos (5) - 1

What is the integral from 0 to 5 of xcos(x) ?
The integral from 0 to 5 of xcos(x) is 5sin(5)+cos(5)-1